Topic: Fluid Mechanics
The specific weight W of ocean water changes according to the equation $W=W_{0}+C\sqrt{h}$ $W_{0}$ = Specific weight of ocean water at free surface and C is a constant. The pressure as a function of depth h is given by
- A. $W_{0}h$
- B. $W_{0}h+(5/2)Ch$
- C. $W_{0}h+(2/3)Ch^{3/2}$
- D. $W_{0}h-(2/3)Ch^{2/3}$
Answer: C. $W_{0}h+(2/3)Ch^{3/2}$
Explanation: Pressure is defined as the integral of specific weight with respect to depth: $P = \int W dh$. Given the specific weight function $W = W_{0} + C\sqrt{h}$, we integrate it: $P = \int (W_{0} + C h^{1/2}) dh = W_{0}h + C \frac{h^{3/2}}{3/2}$. This simplifies to $P = W_{0}h + \frac{2}{3}C h^{3/2}$.